Computing as a utility has been possible with cloud computing technology. Another technology that has evolved with the internet and has become an inseparable part of our lives is the internet of things (IoT). With the growing use of IoT devices, the data generated and used by them is increasing tremendously, and resource-constrained IoT devices can make use of the cloud for data and computing needs. When IoT and cloud converge there are security and privacy issues as the cloud is a shared resource. Access control mechanisms play an important role in maintaining the security of users' data. Attribute-based encryption provides fine-grained access to data, thus ensuring selective access to data. We review the literature on access control mechanisms for cloud-based IoT and provide an analysis of their strengths and weaknesses. We present a comparison of the mechanisms, highlighting the challenges and open research questions in the field of cloud-based IoT access control and provide suggestions for future research and development. Our findings contribute to the understanding of access control mechanisms for cloud-based IoT and provide insights for their selection and deployment in real-world scenarios.